Geodesic
Periods of digit-position sequences received from~linear recurrent sequences of maximal period over finite prime fields
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 62-68.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, for any integer $r\geq 3$, the periods of digit-position sequences obtained from $r$-ary representation of elements in a linear recurrent sequence of the maximal period over prime field are computed.
Keywords: linear recurrent sequences of maximal period, digit-position sequences, finite fields, prime fields, periods of linear recurrent sequences. 
@article{PDM_2015_1_a5,
     author = {S. A. Kuzmin},
     title = {Periods of digit-position sequences received from~linear recurrent sequences of maximal period over finite prime fields},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {62--68},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_1_a5/}
}
TY  - JOUR
AU  - S. A. Kuzmin
TI  - Periods of digit-position sequences received from~linear recurrent sequences of maximal period over finite prime fields
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 62
EP  - 68
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_1_a5/
LA  - ru
ID  - PDM_2015_1_a5
ER  - 
%0 Journal Article
%A S. A. Kuzmin
%T Periods of digit-position sequences received from~linear recurrent sequences of maximal period over finite prime fields
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 62-68
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_1_a5/
%G ru
%F PDM_2015_1_a5
S. A. Kuzmin. Periods of digit-position sequences received from~linear recurrent sequences of maximal period over finite prime fields. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 62-68. http://geodesic.mathdoc.fr/item/PDM_2015_1_a5/

[1] Gluhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 2, Gelios ARV Publ., Moscow, 2003, 416 pp. (in Russian)

[2] Sachkov V. N., Gorchinskij Ju. N., Zubkov A. N., Jablonskij S. V. (eds.), Trudy po Diskretnoi Matematike, 1, TVP Publ., Moscow, 1997, 280 pp. (in Russian) | MR | Zbl

[3] Sachkov V. N., Gorchinskij Ju. N., Zubkov A. N., Jablonskij S. V. (eds.), Trudy po Diskretnoi Matematike, 2, TVP Publ., Moscow, 1998, 314 pp. (in Russian) | MR | Zbl

[4] Zhu X. Y., Qi W.-F., “On the distinctness of modular reductions of maximal length sequences modulo odd prime powers”, Math. Comput., 77:263 (2008), 1623–1637 | DOI | MR | Zbl

[5] Zheng Q.-X., Qi W.-F., “A new result on the distinctness of primitive sequences over $\mathbb Z/{(pq)}$ modulo 2”, Finite Fields Their Appl., 17:3 (2011), 254–274 | DOI | MR | Zbl

[6] Kuz'min A. S., “O periodah razrjadov v $r$-ichnoj sisteme schislenija znakov linejnyh rekurrentnyh posledovatel'nostej nad konechnymi prostymi poljami”, Bezopasnost' Informacionnyh Tehnologij, 1995, no. 4, 71–75 (in Russian)

[7] Gluhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 1, Gelios ARV Publ., Moscow, 2003, 336 pp. (in Russian)